Palestinian emergency services and witnesses said Israel Defense Forces soldiers killed one Palestinian and wounded another near the border with Gaza, Israel Radio reported on Saturday.
Medical officials in Gaza said the man, who was 75 and whose body was only discovered on Saturday when it became light, had been shot several times.
They added that his family had reported he had been missing for two days.
The army spokesman said troops had spotted the man during darkness hours in an area that the military designated a combat zone that is off limits because of many attacks attempted by Palestinian militants on border patrols.
The wounded man, a 22-year-old Palestinian, was hospitalized for treatment.
The latest incidents came as Palestinians and Israeli Arabs commemorated the Nakba, (catastrophe in Arabic), with thousands of Palestinians marching in Gaza to mark 62 years of displacement.
Hundreds of thousands of Palestinians fled or were driven out during the 1948 war surrounding Israel's creation.
In Saturday's rally, Palestinians attempted to overcome their current internal divisions, at least briefly, by protesting together.
Gaza's Hamas rulers marched alongside their bitter rivals Fatah. They waved Palestinian flags and carried a giant key that is symbolic of their hoped-for return.
Some five million Palestinian refugees and their descendants are scattered through the Mideast.
Want to enjoy 'Zen' reading - with no ads and just the article? Subscribe todaySubscribe now